A193604 Augmentation of the triangle A055248. See Comments.

1, 2, 1, 8, 8, 3, 64, 88, 62, 19, 1024, 1664, 1568, 896, 233, 32768, 58368, 64128, 49248, 23890, 5385, 2097152, 3932160, 4703232, 4249728, 2800488, 1179656, 233787, 268435456, 517996544, 649887744, 645547008, 507802304, 293645688, 108978862

Offset: 0

Author

Clark Kimberling, Jul 31 2011

Keywords

• nonn
• tabl

Comments

For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.

Examples

			First five rows of A193604:
1
2.....1
8.....8.....3
64....88....62....19
1024..1664..1568..896...233
		

Crossrefs

Cf. A055248, A193091.

Programs

Mathematica

u[n_, k_] := Sum[Binomial[n, h], {h, 0, k}] (* A055248 *)
p[n_, k_] := u[n, n - k]
Table[p[n, k], {n, 0, 5}, {k, 0, n}]
m[n_] := Table[If[i <= j, p[n + 1 - i, j - i], 0], {i, n}, {j, n + 1}]
TableForm[m[4]]
w[0, 0] = 1; w[1, 0] = p[1, 0]; w[1, 1] = p[1, 1];
v[0] = w[0, 0]; v[1] = {w[1, 0], w[1, 1]};
v[n_] := v[n - 1].m[n]
TableForm[Table[v[n], {n, 0, 6}]] (* A193604 *)
Flatten[Table[v[n], {n, 0, 8}]]